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Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions
Abstract
An exact method for determining the critical percolation probability, pc, for a number of two-dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc = ½. For the bond problem on the triangular, simple quadratic, and honeycomb lattices, pc=2 sin (118π),12,1−2 sin (118π), respectively. A matching theorem for the mean number of finite clusters on certain two-dimensional lattices, somewhat analogous to the duality transformation for the partition function of the Ising model, is described.
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Citations
Cited by
Hopping Conductivity in Disordered Systems
Ambegaokar, V., Halperin, B. I., & Langer, J. S. (1971) · Physical Review B · doi:10.1103/physrevb.4.2612 · Cited by 1,917
Percolation and conductivity: A computer study. I
Pike, G. E., & Seager, C. H. (1974) · Physical Review B · doi:10.1103/physrevb.10.1421 · Cited by 1,031
Essam, J. W. (1980) · Reports on Progress in Physics · doi:10.1088/0034-4885/43/7/001 · Cited by 1,018
Self-citationPercolation on complex networks: Theory and application
Li, M., Liu, R.-R., Lü, L., Hu, M.-B., Xu, S., & Zhang, Y.-C. (2021) · Physics Reports · doi:10.1016/j.physrep.2020.12.003 · Cited by 365
Metadata
- Authors
- Sykes, M. F., & Essam, J. W.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1964-08-01
- Volume
- 5
- Issue
- 8
- Pages
- 1117-1127
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1972850107
- Cited by
- 601
- References
- 0
- FWCI
- 1.01
- Type
- journal article
- Language
- en
- Open access
- closed
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- Sykes, M. F., & Essam, J. W. (1964). Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions. Journal of Mathematical Physics. https://doi.org/10.1063/1.1704215
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